I would persuade them by using the following points-
1. Charity begins at Home! To help these innocent and speechless creatures is the best way to get love and good wishes.
2. Pets in house can keep everybody healthy and can help them to be punctual.
3. Friendship with the animals is the best of all other friendships because they are always honest to us and would not harm anyone.
4. Also spending time with pets helps to know more about their life and playing with them is really fun!
First i would think about it and it effects and its harms and if i like them or i want them to be them  as my pet i would say my parents about it and i would say my parents mum dont be tense or worry they wont harm me and i would say  my mother you allow me  to keep them for atleast 2 days if they harm any one then i will throw it mum belive me .These  i would  say to my parents . hope u like it dear 
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you should keep your feelings in front of your parents about your love for animals and care for them